Efficient parallel processing of a network with conflict constraints between nodes

ABSTRACT

According to one exemplary embodiment, a method for parallel processing a network of nodes having at least one ordering constraint and at least one conflict constraint is provided. The method may include breaking a plurality of loops caused by the at least one ordering constraint. The method may also include determining a node order based on the at least one ordering constraint. The method may then include determining a conflict order based on the at least one conflict constraint, whereby no new loops are created in the network. The method may further include performing parallel processing of the network of nodes based on the node order and the conflict order.

BACKGROUND

The present invention relates generally to the field of computing, andmore particularly to processing networks with conflict constraintsbetween nodes.

Circuit analysis techniques are employed to determine if a circuit meetspredefined specifications. Processing a large network with nodes is acomputationally expensive task, taxing compute resources. Many types oflarge network processing may be done by processing each node within thenetwork. Static timing analysis computes the arrival time for each nodeof the network. Static noise analysis computes noise pulse and/or deltadelay for each sink of each net in the network.

SUMMARY

According to one exemplary embodiment, a method for parallel processinga network of nodes having at least one ordering constraint and at leastone conflict constraint is provided. The method may include breaking aplurality of loops caused by the at least one ordering constraint. Themethod may also include determining a node order based on the at leastone ordering constraint. The method may then include determining aconflict order based on the at least one conflict constraint, whereby nonew loops are created in the network. The method may further includeperforming parallel processing of the network of nodes based on the nodeorder and the conflict order.

According to another exemplary embodiment, a computer system forparallel processing a network of nodes having at least one orderingconstraint and at least one conflict constraint is provided. Thecomputer system may include one or more processors, one or morecomputer-readable memories, one or more computer-readable tangiblestorage devices, and program instructions stored on at least one of theone or more storage devices for execution by at least one of the one ormore processors via at least one of the one or more memories, wherebythe computer system is capable of performing a method. The method mayinclude breaking a plurality of loops caused by the at least oneordering constraint. The method may also include determining a nodeorder based on the at least one ordering constraint. The method may theninclude determining a conflict order based on the at least one conflictconstraint, whereby no new loops are created in the network. The methodmay further include performing parallel processing of the network ofnodes based on the node order and the conflict order.

According to yet another exemplary embodiment, a computer programproduct for parallel processing a network of nodes having at least oneordering constraint and at least one conflict constraint is provided.The computer program product may include one or more computer-readablestorage devices and program instructions stored on at least one of theone or more tangible storage devices, the program instructionsexecutable by a processor. The computer program product may includeprogram instructions to break a plurality of loops caused by the atleast one ordering constraint. The computer program product may alsoinclude program instructions to determine a node order based on the atleast one ordering constraint. The computer program product may theninclude program instructions to determine a conflict order based on theat least one conflict constraint, whereby no new loops are created inthe network. The computer program product may further include programinstructions to perform parallel processing of the network of nodesbased on the node order and the conflict order.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

These and other objects, features and advantages of the presentinvention will become apparent from the following detailed descriptionof illustrative embodiments thereof, which is to be read in connectionwith the accompanying drawings. The various features of the drawings arenot to scale as the illustrations are for clarity in facilitating oneskilled in the art in understanding the invention in conjunction withthe detailed description. In the drawings:

FIG. 1 illustrates a networked computer environment according to atleast one embodiment;

FIG. 2A is an operational flow chart illustrating a process for networkparallel processing according to at least one embodiment;

FIG. 2B is an operational flow chart illustrating a process for nodeordering according to at least one embodiment;

FIG. 3 illustrates an example cell network according to at least oneembodiment;

FIG. 4 illustrates an example strictly ordered graph based on arbitraryordering according to at least one embodiment;

FIG. 5 illustrates an example strictly ordered graph based on costestimate according to at least one embodiment;

FIG. 6 is a block diagram of internal and external components ofcomputers and servers depicted in FIG. 1 according to at least oneembodiment;

FIG. 7 is a block diagram of an illustrative cloud computing environmentincluding the computer system depicted in FIG. 1, in accordance with anembodiment of the present disclosure; and

FIG. 8 is a block diagram of functional layers of the illustrative cloudcomputing environment of FIG. 7, in accordance with an embodiment of thepresent disclosure.

DETAILED DESCRIPTION

Detailed embodiments of the claimed structures and methods are disclosedherein; however, it can be understood that the disclosed embodiments aremerely illustrative of the claimed structures and methods that may beembodied in various forms. This invention may, however, be embodied inmany different forms and should not be construed as limited to theexemplary embodiments set forth herein. Rather, these exemplaryembodiments are provided so that this disclosure will be thorough andcomplete and will fully convey the scope of this invention to thoseskilled in the art. In the description, details of well-known featuresand techniques may be omitted to avoid unnecessarily obscuring thepresented embodiments.

The present invention may be a system, a method, and/or a computerprogram product. The computer program product may include a computerreadable storage medium (or media) having computer readable programinstructions thereon for causing a processor to carry out aspects of thepresent invention.

The computer readable storage medium can be a tangible device that canretain and store instructions for use by an instruction executiondevice. The computer readable storage medium may be, for example, but isnot limited to, an electronic storage device, a magnetic storage device,an optical storage device, an electromagnetic storage device, asemiconductor storage device, or any suitable combination of theforegoing. A non-exhaustive list of more specific examples of thecomputer readable storage medium includes the following: a portablecomputer diskette, a hard disk, a random access memory (RAM), aread-only memory (ROM), an erasable programmable read-only memory (EPROMor Flash memory), a static random access memory (SRAM), a portablecompact disc read-only memory (CD-ROM), a digital versatile disk (DVD),a memory stick, a floppy disk, a mechanically encoded device such aspunch-cards or raised structures in a groove having instructionsrecorded thereon, and any suitable combination of the foregoing. Acomputer readable storage medium, as used herein, is not to be construedas being transitory signals per se, such as radio waves or other freelypropagating electromagnetic waves, electromagnetic waves propagatingthrough a waveguide or other transmission media (e.g., light pulsespassing through a fiber-optic cable), or electrical signals transmittedthrough a wire.

Computer readable program instructions described herein can bedownloaded to respective computing/processing devices from a computerreadable storage medium or to an external computer or external storagedevice via a network, for example, the Internet, a local area network, awide area network and/or a wireless network. The network may comprisecopper transmission cables, optical transmission fibers, wirelesstransmission, routers, firewalls, switches, gateway computers and/oredge servers. A network adapter card or network interface in eachcomputing/processing device receives computer readable programinstructions from the network and forwards the computer readable programinstructions for storage in a computer readable storage medium withinthe respective computing/processing device.

Computer readable program instructions for carrying out operations ofthe present invention may be assembler instructions,instruction-set-architecture (ISA) instructions, machine instructions,machine dependent instructions, microcode, firmware instructions,state-setting data, or either source code or object code written in anycombination of one or more programming languages, including an objectoriented programming language such as Smalltalk, C++ or the like, andconventional procedural programming languages, such as the “C”programming language or similar programming languages. The computerreadable program instructions may execute entirely on the user'scomputer, partly on the user's computer, as a stand-alone softwarepackage, partly on the user's computer and partly on a remote computeror entirely on the remote computer or server. In the latter scenario,the remote computer may be connected to the user's computer through anytype of network, including a local area network (LAN) or a wide areanetwork (WAN), or the connection may be made to an external computer(for example, through the Internet using an Internet Service Provider).In some embodiments, electronic circuitry including, for example,programmable logic circuitry, field-programmable gate arrays (FPGA), orprogrammable logic arrays (PLA) may execute the computer readableprogram instructions by utilizing state information of the computerreadable program instructions to personalize the electronic circuitry,in order to perform aspects of the present invention.

Aspects of the present invention are described herein with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems), and computer program products according to embodiments of theinvention. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer readable program instructions.

These computer readable program instructions may be provided to aprocessor of a general purpose computer, special purpose computer, orother programmable data processing apparatus to produce a machine, suchthat the instructions, which execute via the processor of the computeror other programmable data processing apparatus, create means forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks. These computer readable program instructionsmay also be stored in a computer readable storage medium that can directa computer, a programmable data processing apparatus, and/or otherdevices to function in a particular manner, such that the computerreadable storage medium having instructions stored therein comprises anarticle of manufacture including instructions which implement aspects ofthe function/act specified in the flowchart and/or block diagram blockor blocks.

The computer readable program instructions may also be loaded onto acomputer, other programmable data processing apparatus, or other deviceto cause a series of operational steps to be performed on the computer,other programmable apparatus or other device to produce a computerimplemented process, such that the instructions which execute on thecomputer, other programmable apparatus, or other device implement thefunctions/acts specified in the flowchart and/or block diagram block orblocks.

The flowchart and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods, and computer program products according to variousembodiments of the present invention. In this regard, each block in theflowchart or block diagrams may represent a module, segment, or portionof instructions, which comprises one or more executable instructions forimplementing the specified logical function(s). In some alternativeimplementations, the functions noted in the block may occur out of theorder noted in the figures. For example, two blocks shown in successionmay, in fact, be executed substantially concurrently, or the blocks maysometimes be executed in the reverse order, depending upon thefunctionality involved. It will also be noted that each block of theblock diagrams and/or flowchart illustration, and combinations of blocksin the block diagrams and/or flowchart illustration, can be implementedby special purpose hardware-based systems that perform the specifiedfunctions or acts or carry out combinations of special purpose hardwareand computer instructions.

The following described exemplary embodiments provide a system, methodand program product for efficient parallel processing of a network withconflict constraints between nodes. Additionally, the present embodimenthas the capacity to improve the technical field of parallel networkprocessing with conflict constraints between nodes by ordering conflictconstraints such that no new loops are created in the network.

As previously described, analyzing large networks is computationallyexpensive. In order to improve network analysis efficiency, the networkmay be processed in parallel. Parallel processing may still be fraughtwith complexities in large networks since networks may have nodeordering constraints. For example, the arrival time of a cell input mayhave to be computed before the cell output. Ordering constraints maycreate computation complexities due to loop formation (e.g., transparentlatches in static timing analysis). Cyclic dependencies require loopcutting and iterative processing to obtain the most accurate answer.However, iteration and loop cutting may also significantly impactprocess efficiency. Although some pairs of nodes may not have anordering requirement, the pair of nodes may create parallel processingconflicts when two nodes may access and update the same data (e.g.,noise analysis between coupled nets). Similarly to loop cutting,conflicts may be processed by using iterations. For example, one end maybe chosen to process first and a new iteration may be used if processinga second node causes changes that could affect the first node processed.

Therefore, it may be advantageous to, among other things, provide a wayto efficiently manage parallel processing conflicts found in networks.

Efficient node ordering may handle conflicts effectively such that nodesare only processed when all predecessor nodes have already beenprocessed. By ordering nodes in this manner, no new loops are created(reducing resources to iterate and reprocess nodes), nodes are processedwith the latest data available (i.e., data is not stale), side copies ofdata are avoided that may cause added complexity and memory usage, andlocking techniques may be avoided that may have significant drawbacks(e.g., hurt scaling, create deadlock, cause unpredictable results,etc.). The network to be analyzed may be represented, for example, as amixed graph having nodes corresponding to nets, directed edgescorresponding to cell input/output connections and undirected edgescorresponding to coupling caps. According to at least one embodiment,managing parallel processing conflict constraints may include the stepsof loop cutting, determining an ordering of nodes, order each conflictbetween a pair of nodes consistent with the determined ordering, andparallel processing the network according to the ordering constraint andconflict constraint.

First, cyclic dependencies within the graph representing the network maybe eliminated using loop cutting techniques. Loops may be cut, asneeded, considering only the ordering constraints (i.e., directed edgeswithin a graph representation) using known techniques.

Next, an ordering of nodes may be determined. Ordering of nodes may bedone by first determining a partial ordering based on the directed edgesof the graph, and then determining a strict ordering between any pairsof conflicting nodes (i.e., nodes whose order was not determined bypartial ordering).

Partial node ordering may be determined by annotating the nodes withinthe graph with additional information to allow any possible dependencyby determining a series of ordering constraints (i.e., directed edgesbetween nodes). Techniques for achieving partial ordering may includelevelization or dependency hashing. Levelization may be implemented byassigning a level number value to each node, whereby the level number ofthe node is greater than or equal to the level numbers of the node'simmediate predecessors (e.g., A cannot depend on B unlesslevel(A)>level(B)). Dependency hashing may assign arbitrary bit stringsto each primary node (i.e., a node with no predecessors). The bit stringof successive nodes may then contain the bit strings of the successivenode's predecessor nodes. For example, node A cannot depend on node B ifany bit on B is also set on A (i.e., if bits(A) & ˜bits(A) !=0).

The nodes of the graph may also given a strict (i.e., total) ordering.Strict node ordering may be used to determine a node ordering forconflicts whose ordering was not determined by partial node orderingwhile ensuring that no new loops are created as a result of strict nodeordering.

According to at least one embodiment, implementation of strict orderingmay be accomplished by assigning each node within the graph a name orpointer value (e.g., to the memory location storing the node). Then, thenodes may be arbitrarily ordered to resolve ambiguities based on thenode's name or pointer value such that no possible dependency may becreated. For example, a node with a smaller pointer value may be orderedbefore another node with a greater pointer value.

According to at least one other embodiment, strict ordering of nodes maybe based on the estimated cost of processing the node. Conflicting nodesmay be ordered by processing the node having the largest cost first.Processing the largest cost node first may reduce the likelihood ofthreads running out of nodes to process. Conflicting nodes may also beprocessed such that the node with the largest cost is processed last. Byusing the most up-to-date (i.e., least stale) information for the nodethat has the most dependencies, there may be less of a likelihood ofhaving to reprocess the costly node later. The choice between processingthe highest cost node first or last may be made based on the number ofthreads and nodes (i.e., average available parallelism) or theimportance of getting the most accurate answers and if iterations willbe employed. Additionally, estimating the processing cost of a node mayinclude the share of the total cumulative cost of all downstream nodes.

According to yet another embodiment, strict ordering of nodes may bedetermined by the criticality of each node (i.e., the importance ofgetting the most accurate result). Thus, node conflicts may be orderedsuch that the most critical end may be processed last. Critical nodesmay then be processed using the most up-to-date (i.e., least stale)information.

Then, each conflict between a pair of nodes may be ordered. Orderingconflicts between two nodes (i.e., assigning a direction to anundirected edge within a graph representation of the network) may behandled by following the partial ordering or by following the strictordering determined previously. According to at least one embodiment,conflicts may be ordered according to the partial ordering if there maybe a possible dependency between two nodes; otherwise the conflicts maybe ordered consistent with strict ordering.

Once an order has been determined for the node conflicts, parallelprocessing of the nodes may commence consistent with the originalordering constraints and the order chosen for conflicting edgespreviously. Parallel processing may proceed using a known process, suchas multi-threaded dynamic scheduling (MTDS).

Referring now to FIG. 1, an exemplary networked computer environment 100in accordance with one embodiment is depicted. The networked computerenvironment 100 may include a computer 102 with a processor 104 and adata storage device 106 that is enabled to run a network parallelprocessing program 108 a. The networked computer environment 100 mayalso include a server 110 that is enabled to run a network parallelprocessing program 108 b and a communication network 112. The networkedcomputer environment 100 may include a plurality of computers 102 andservers 110, only one of which is shown for illustrative brevity. Thecommunication network may include various types of communicationnetworks, such as a wide area network (WAN), local area network (LAN), atelecommunication network, a wireless network, a public switched networkand/or a satellite network. It may be appreciated that FIG. 1 providesonly an illustration of one implementation and does not imply anylimitations with regard to the environments in which differentembodiments may be implemented. Many modifications to the depictedenvironments may be made based on design and implementationrequirements.

The client computer 102 may communicate with server computer 110 via thecommunications network 112. The communications network 112 may includeconnections, such as wire, wireless communication links, or fiber opticcables. As will be discussed with reference to FIG. 4, server computer110 may include internal components 902 a and external components 904 a,respectively and client computer 102 may include internal components 902b and external components 904 b, respectively. Client computer 102 maybe, for example, a mobile device, a telephone, a PDA, a netbook, alaptop computer, a tablet computer, a desktop computer, or any type ofcomputing device capable of running a program and accessing a network.

A program, such as a network parallel processing program 108 a and 108 bmay run on the client computer 102 or on the server computer 110. Thenetwork parallel processing program 108 a and 108 b may be used toefficiently process networks containing conflict constraints betweennodes. The network parallel processing program 108 a and 108 b isexplained in further detail below with respect to FIGS. 2A and 2B.

Referring now to FIG. 2A, an operational flow chart illustrating theexemplary node ordering process 200 by the network parallel processingprogram 108 a and 108 b (FIG. 1) according to at least one embodiment isdepicted.

At 202, the node ordering process 200 may break loops caused by orderingconstraints within the network. According to at least one embodiment,the node ordering process 200 may determine loops (i.e., cyclicdependencies) exist within a network based on the ordering constraints.Ordering constraints may be determined by mapping the input and outputconnections of a node in the network. For example, in a cell network, acell with an input and an output has an ordering constraint thatindicates that the input must be processed before the output. A loop(i.e., cyclic dependency) may occur with a transparent latch in statictiming analysis. Loop cutting may be performed by a known loop cuttingalgorithm.

Next, at 204, an ordering for the nodes in the network may bedetermined. Node ordering will be discussed in further detail below withrespect to FIG. 2B.

Then, at 206 an order for each conflict constraint may be determined.Conflict constraints may be an undirected edge between two nodes withinthe graph representing the network. The conflict constraint maycorrespond to, for example, coupling capacitors in a circuit. Accordingto at least one embodiment, the conflict constraints (i.e., undirectededges) may be given an order (i.e., undirected edges given a direction)between the two nodes (e.g., node A and node B). In cases when the twonodes connected to the conflict constraint edge were ordered previouslyas part of the partial ordering (e.g., using a levelization scheme) andthe two nodes had a distinct order (e.g., node A was assigned level 3and node B was assigned level 4), the conflict edge may be given adirection from lower ordered node to the higher ordered node (e.g., nodeA would be processed before node B). However, if the two nodes connectedto the conflict edge were ambiguously ordered during partial ordering(e.g., node A and node B were both assigned level 3), then the conflictconstraint edge may be given a direction from the lower ordered node tothe higher ordered node based on the strict node order (e.g., based onnode criticality).

At, 208, the nodes in the network may be processed in parallel based onthe determined node order. According to at least one embodiment,parallel processing may be accomplished using a known method such asmulti-threaded dynamic scheduling (MTDS).

Referring now to FIG. 2B, an operational flow chart illustrating indetail the exemplary node ordering steps of the node ordering process200.

At 210, a partial node ordering may be determined. According to at leastone embodiment, the nodes may be annotated with additional informationto allow for any potential dependency through a series of orderingconstraints. Partial ordering may result in nodes being ordered beforeor after other nodes and some nodes may still be ambiguous (e.g.,between two nodes, which node should be ordered before the other nodemay not be determined). Annotation of nodes with additional informationmay be done through processes such as, for example, levelization ordependency hashing.

According to at least one implementation, levelization may beimplemented by assigning a level value (e.g., a number) to each nodesuch that a successor node (i.e., endpoint node) has a number that isgreater than the level numbers of the nodes preceding the successornode. For example, a predecessor node may be assigned a level number of3. The predecessor node's immediate successor node may then be assigneda level number of 4. With nodes assigned the level number according to alevelization scheme, node A cannot depend on node B unless the levelassigned to A exceeds the level assigned to node B.

Alternatively, dependency hashing may be used to annotate nodes.Dependency hashing may be implemented by assigning an arbitrary bitstring to each primary input node (i.e., node with no predecessor nodes)in the network. Each internal node (i.e., nodes having a predecessornode) may be assigned a bit string that may contain the bit string ofthe preceding nodes (i.e., the bit string for an internal node is OR ofbit strings of the node's immediate predecessors). Once the nodes havebeen assigned bit strings according to the dependency hashing scheme,node A cannot depend on node B if any bit set on B is not also set on A(i.e., if bits(B) & ˜bits(A) !=0).

After partial ordering, some nodes in the graph may not be completelyordered in relation to other nodes. For example, if a levelizationscheme is used, two nodes may be at the same level in the graph (e.g.,node A and node B are both assigned the level number 3). Thus, nodespreceding and succeeding the nodes may be ordered, however the two (ormore) nodes having the same level value (e.g., node A and node B) maycreate an ambiguity as to which node would be processed first (i.e., tiebetween two or more nodes). Nodes with ambiguous ordering may beconsidered ambiguous nodes.

Next, at 212 ordering criterion for use in strict node ordering may bedetermined. Depending on the strict ordering scheme that will be used,different criterion for strict ordering may need to be determined.According to at least one embodiment, if the strict ordering scheme thatwill be used is arbitrary (e.g., based on name or pointer value), theordering criterion may include fetching the names or pointer values.

According to at least one other embodiment, if processing cost estimatesare used to determine strict node order, the processing cost for eachnode in the graph may be estimated. Node processing costs may beestimated based on, for example, the number of circuit elements withinthe net (i.e., wire connections between elements) represented by a nodeand may include the node's share of the cumulative cost of processingall downstream nodes.

According to yet another embodiment, if the criticality of each node isused to determine strict node order, the criticality of each node in thegraph may be determined. Node criticality may be determined, forexample, by performing a preliminary analysis of the network. Thepreliminary analysis of the network may include a timing analysis of thenetwork without noise and then making a rough estimate using noise.

Then, at 214 the nodes in the graph may be assigned a strict node order.According to at least one embodiment, the node ordering process 200 maythen augment the partial ordering to provide a strict (i.e., complete)ordering for all nodes in the graph. In order to resolve ambiguitiesresulting from partial node order (i.e., break ties between nodes), anarbitrary scheme may be employed such as using the name or pointer valuefor the nodes to resolve ambiguities based on the determined criterionfrom 212. For example, a pointer value associated with a node may beassociated with a memory address. The memory addresses associated withthe each ambiguous node in a pair of ambiguous nodes may be compared andthe node having the smaller memory address value may be ordered beforethe other ambiguous node having a larger memory address value.

According to at least one other embodiment, strict ordering may beimplemented based on the processing cost of the ambiguous nodes. Oncenode processing cost is estimated (i.e., at 212), conflicting nodes maybe ordered by processing the largest cost node first, ordering thelargest cost node last, or a mix of both approaches. Processing theconflicting node having the largest cost first may be done to reduce thelikelihood of threads running out of work to do. The node having thelargest processing cost may be ordered to be processed last in order touse the most up-to-date (i.e., least stale) information for the nodehaving the most dependencies. In a mixed approach, ordering the nodehaving the largest cost first or last may depend on the number ofthreads and nodes (average available parallelism), the importance ofgetting the most accurate answers and whether there may be iteration.For example, if there may be iteration, processing the largest cost nodelast may be more efficient as the largest cost node may not consume moreresources by being reprocessed. Additionally, another mixed approach mayspecify that the largest cost node having a processing cost below apredetermined threshold may be processed first and if the processingcost exceeds the predetermined threshold, the largest cost node may beprocessed last.

According to yet another embodiment, strict ordering may be implementedby resolving conflicts based on the criticality of the node. Based onthe preliminary analysis performed at 212, nodes may be identified thatmay be close to being critical (i.e., close to having zero slack). Nodesthat are close to being critical may be processed last since criticalnodes may need the most up-to-date (i.e., least stale) information.

Referring now to FIG. 3, an example cell network 300 is depicted. Thecell network 300 includes multiple nets 302 a-i, cells 304 a-f andcoupling capacitors 306 a-c.

Referring now to FIG. 4, an example of a first strictly ordered graph400 based on the cell network 300 (FIG. 3) is depicted. A mixed graph(i.e., graph with directed edges and undirected edges) is firstgenerated based on the cell network 300 (FIG. 3) containing a graph node402 a-i for each net 302 a-i (FIG. 3). Cell 304 a-f (FIG. 3)input/output (I/O) connections from the cell network 300 (FIG. 3) arerepresented in the graph as directed edges 404 a-h (i.e., orderingconstraints). Additionally, the coupling capacitors 306 a-c (FIG. 3) arerepresented as conflict edges 406 a-c. Utilizing a levelization schemeas described above previously, levels 408 may be assigned to the nodesin the graph. After partial ordering using levelization, some conflictedges may remain unordered (i.e., undirected) such as conflict edge 406a. Levelization would not order conflict edge 406 a since the nodes(i.e., nodes 402 e and 4020 at each end of the conflict edge 406 a havethe same level value (i.e., level 1). Therefore, a strict orderingscheme (i.e., 214: FIG. 2B), such as arbitrarily ordering the nodesbased on node name, is used to transform the mixed graph into the firststrictly ordered graph 400 as depicted by assigning a direction to thefinal undirected conflict edge 406 a. With all edges having an assigneddirection and no loops within the graph, the first strictly orderedgraph 400 would also have the qualities of a directed acyclic graph.

Based on the first strictly ordered graph 400, a possible firstprocessing order 410 for the nodes 402 a-i distributed among two threadsmay be generated. Given the first strictly ordered graph 400, nodes 402h and 402 i may be processed by the two threads since both nodes have nopredecessor nodes that are not ready (since the nodes have nopredecessor nodes). After processing nodes 402 h and 402 i, node 402 gwould be processed by thread 1 (since node 402 g has no predecessornodes and therefore no predecessor nodes that are not ready), howevernode 402 f would not be processed by thread 2 due to a conflict in thenode order with node 402 e. In other words, node 402 f has predecessornodes that are not ready for processing (i.e., node 402 e) due to theorder of the conflict edge 406 a and thus thread 2 would be idle. Afterthread 1 finishes processing node 402 g, thread 1 would process node 402e as node 402 g, the predecessor node for node 402 e, was processed andready. After 402 e is processed, 402 f could then be processed, sinceall predecessor nodes to node 402 f are ready and the conflict with node402 e was resolved. Thread 2 would then process node 402 c. Thread 1would process node 402 d and due to a conflict between node 402 d and402 a, 402 a would not be processed leaving thread 2 idle. Finally,thread 1 would process node 402 a and thread 2 would process 402 b. Dueto unresolved conflicts, the first processing order 410 leaves thread 2idle for three steps and takes six steps to complete.

Referring now to FIG. 5, an example of a second strictly ordered graph500 based on cost estimate ordering is depicted. The second strictlyordered graph 500 is generated from the mixed graph described abovewhere the undirected conflict edges have been assigned a direction. Theundirected conflict edges are assigned a direction as described aboveusing levelization for partial node ordering (i.e., 210: FIG. 2B).

Some undirected conflict edges may be assigned a direction based onpartial node ordering. The undirected conflict edges spanning betweennodes 402 e and 402 a, and nodes 402 e and 402 a are assigned differentlevel numbers based on the levelization partial node ordering scheme(level 1 and level 3 respectively). Thus, the direction given to theundirected conflict edge between nodes 402 e and 402 a would be from thenode with the lower level number (i.e., node 402 e at level 1) to thenode with the higher level number (i.e., node 402 a at level 3).Resulting in conflict edge 502 b starting at node 402 e and ending atnode 402 a. The resulting direction for the conflict edge 502 b preventsformation of a loop that would occur if the direction had been reversed(e.g., starting from node 402 a and ending at node 402 e).

Similarly, the undirected conflict edge that spans between nodes 402 dand 402 a would be assigned a direction from node 402 d to node 402 asince node 402 d has a level number of 2 and node 402 a has a levelnumber of 3. The resulting conflict edge 502 c would start at node 402 dand end at node 402 a. In other words, node 402 a would depend on node402 d and therefore 402 d must be processed before node 402 a.

After partial node ordering (i.e., 210: FIG. 2B), the ordering criterionfor the strict order scheme to be used is then determined (i.e., 212:FIG. 2B). Given an estimate of processing cost strict ordering scheme,the cost of processing each node is estimated. Then the unresolvedconflicts (i.e., the conflict edge between nodes 402 e and 402 f) aredetermined based on the processing cost estimate for the nodes at theends of the conflict edge. In the depicted example, node 402 e wouldprecede 402 f based on estimating the cost of processing. Therefore, theundirected conflict edge between nodes 402 e and 402 f would becomeconflict edge 502 a having a direction starting from node 402 e andending at node 402 f. In other words, 402 f would depend on node 402 eand thus node 402 e would be ordered for processing before node 402 fsatisfying the conflict constraint. After giving a direction to alledges of the mixed graph, and ensuring that no new cycles have beencreated, the resulting second strictly ordered graph 500 also has thequalities of a directed acyclic graph.

Based on the second strictly ordered graph 500, the possible secondprocessing order 504 using two threads may begin with thread 1processing node 402 g and thread 2 processing node 402 h at the firststep. At the second step, thread 1 may process node 402 i and thread 2may process node 402 e. At the third step thread 1 may process node 402c and thread 2 may process 402 f. Then, at step four, thread 1 mayprocess 402 d and thread 2 may be idle. Out of the remaining nodes(i.e., node 402 a and node 402 b) neither node has all node predecessorsready (i.e., already processed) and thus thread 2 would have no node toprocess and would be idle. Finally, at step five, thread 1 may processnode 402 a and thread 2 may process node 402 b since node 402 d wasprocessed at the previous step, resulting in all predecessor nodes tonodes 402 a and 402 b being ready. Thus, all nodes 402 a-i in the secondstrictly ordered graph 500 may be processed in five steps with a singlethread that was idle for one step (i.e., thread 2 at step four).

It may be appreciated that FIGS. 2A, 2B, 3, 4 and 5 provide only anillustration of a few embodiments and does not imply any limitationswith regard to how different embodiments may be implemented. Thedepicted embodiments describe applications relating to circuit analysis,however the process described above may apply to various other domains.Many modifications to the depicted embodiment(s) may be made based ondesign and implementation requirements.

FIG. 6 is a block diagram 900 of internal and external components ofcomputers depicted in FIG. 1 in accordance with an illustrativeembodiment of the present invention. It should be appreciated that FIG.6 provides only an illustration of one implementation and does not implyany limitations with regard to the environments in which differentembodiments may be implemented. Many modifications to the depictedenvironments may be made based on design and implementationrequirements.

Data processing system 902, 904 is representative of any electronicdevice capable of executing machine-readable program instructions. Dataprocessing system 902, 904 may be representative of a smart phone, acomputer system, PDA, or other electronic devices. Examples of computingsystems, environments, and/or configurations that may represented bydata processing system 902, 904 include, but are not limited to,personal computer systems, server computer systems, thin clients, thickclients, hand-held or laptop devices, multiprocessor systems,microprocessor-based systems, network PCs, minicomputer systems, anddistributed cloud computing environments that include any of the abovesystems or devices.

User client computer 102 (FIG. 1), and network server 110 (FIG. 1) mayinclude respective sets of internal components 902 a, b and externalcomponents 904 a, b illustrated in FIG. 6. Each of the sets of internalcomponents 902 a, b includes one or more processors 906, one or morecomputer-readable RAMs 908 and one or more computer-readable ROMs 910 onone or more buses 912, and one or more operating systems 914 and one ormore computer-readable tangible storage devices 916. The one or moreoperating systems 914 and programs such as a network parallel processingprogram 108 a and 108 b (FIG. 1), may be stored on one or morecomputer-readable tangible storage devices 916 for execution by one ormore processors 906 via one or more RAMs 908 (which typically includecache memory). In the embodiment illustrated in FIG. 6, each of thecomputer-readable tangible storage devices 916 is a magnetic diskstorage device of an internal hard drive. Alternatively, each of thecomputer-readable tangible storage devices 916 is a semiconductorstorage device such as ROM 910, EPROM, flash memory or any othercomputer-readable tangible storage device that can store a computerprogram and digital information.

Each set of internal components 902 a, b also includes a R/W drive orinterface 918 to read from and write to one or more portablecomputer-readable tangible storage devices 920 such as a CD-ROM, DVD,memory stick, magnetic tape, magnetic disk, optical disk orsemiconductor storage device. The network parallel processing program108 a and 108 b (FIG. 1) can be stored on one or more of the respectiveportable computer-readable tangible storage devices 920, read via therespective R/W drive or interface 918 and loaded into the respectivehard drive 916.

Each set of internal components 902 a, b may also include networkadapters (or switch port cards) or interfaces 922 such as a TCP/IPadapter cards, wireless wi-fi interface cards, or 3G or 4G wirelessinterface cards or other wired or wireless communication links. Thenetwork parallel processing program 108 a (FIG. 1) in client computer102 (FIG. 1) and the network parallel processing program 108 b (FIG. 1)in network server computer 110 (FIG. 1) can be downloaded from anexternal computer (e.g., server) via a network (for example, theInternet, a local area network or other, wide area network) andrespective network adapters or interfaces 922. From the network adapters(or switch port adaptors) or interfaces 922, the network parallelprocessing program 108 a (FIG. 1) in client computer 102 (FIG. 1) andthe network parallel processing program 108 b (FIG. 1) in network servercomputer 110 (FIG. 1) are loaded into the respective hard drive 916. Thenetwork may comprise copper wires, optical fibers, wirelesstransmission, routers, firewalls, switches, gateway computers and/oredge servers.

Each of the sets of external components 904 a, b can include a computerdisplay monitor 924, a keyboard 926, and a computer mouse 928. Externalcomponents 904 a, b can also include touch screens, virtual keyboards,touch pads, pointing devices, and other human interface devices. Each ofthe sets of internal components 902 a, b also includes device drivers930 to interface to computer display monitor 924, keyboard 926 andcomputer mouse 928. The device drivers 930, R/W drive or interface 918and network adapter or interface 922 comprise hardware and software(stored in storage device 916 and/or ROM 910).

It is understood in advance that although this disclosure includes adetailed description on cloud computing, implementation of the teachingsrecited herein are not limited to a cloud computing environment. Rather,embodiments of the present invention are capable of being implemented inconjunction with any other type of computing environment now known orlater developed.

Cloud computing is a model of service delivery for enabling convenient,on-demand network access to a shared pool of configurable computingresources (e.g. networks, network bandwidth, servers, processing,memory, storage, applications, virtual machines, and services) that canbe rapidly provisioned and released with minimal management effort orinteraction with a provider of the service. This cloud model may includeat least five characteristics, at least three service models, and atleast four deployment models.

Characteristics are as follows:

On-demand self-service: a cloud consumer can unilaterally provisioncomputing capabilities, such as server time and network storage, asneeded automatically without requiring human interaction with theservice's provider.

Broad network access: capabilities are available over a network andaccessed through standard mechanisms that promote use by heterogeneousthin or thick client platforms (e.g., mobile phones, laptops, and PDAs).

Resource pooling: the provider's computing resources are pooled to servemultiple consumers using a multi-tenant model, with different physicaland virtual resources dynamically assigned and reassigned according todemand. There is a sense of location independence in that the consumergenerally has no control or knowledge over the exact location of theprovided resources but may be able to specify location at a higher levelof abstraction (e.g., country, state, or datacenter).

Rapid elasticity: capabilities can be rapidly and elasticallyprovisioned, in some cases automatically, to quickly scale out andrapidly released to quickly scale in. To the consumer, the capabilitiesavailable for provisioning often appear to be unlimited and can bepurchased in any quantity at any time.

Measured service: cloud systems automatically control and optimizeresource use by leveraging a metering capability at some level ofabstraction appropriate to the type of service (e.g., storage,processing, bandwidth, and active user accounts). Resource usage can bemonitored, controlled, and reported providing transparency for both theprovider and consumer of the utilized service.

Service Models are as follows:

Software as a Service (SaaS): the capability provided to the consumer isto use the provider's applications running on a cloud infrastructure.The applications are accessible from various client devices through athin client interface such as a web browser (e.g., web-based e-mail).The consumer does not manage or control the underlying cloudinfrastructure including network, servers, operating systems, storage,or even individual application capabilities, with the possible exceptionof limited user-specific application configuration settings.

Platform as a Service (PaaS): the capability provided to the consumer isto deploy onto the cloud infrastructure consumer-created or acquiredapplications created using programming languages and tools supported bythe provider. The consumer does not manage or control the underlyingcloud infrastructure including networks, servers, operating systems, orstorage, but has control over the deployed applications and possiblyapplication hosting environment configurations.

Infrastructure as a Service (IaaS): the capability provided to theconsumer is to provision processing, storage, networks, and otherfundamental computing resources where the consumer is able to deploy andrun arbitrary software, which can include operating systems andapplications. The consumer does not manage or control the underlyingcloud infrastructure but has control over operating systems, storage,deployed applications, and possibly limited control of select networkingcomponents (e.g., host firewalls).

Deployment Models are as follows:

Private cloud: the cloud infrastructure is operated solely for anorganization. It may be managed by the organization or a third party andmay exist on-premises or off-premises.

Community cloud: the cloud infrastructure is shared by severalorganizations and supports a specific community that has shared concerns(e.g., mission, security requirements, policy, and complianceconsiderations). It may be managed by the organizations or a third partyand may exist on-premises or off-premises.

Public cloud: the cloud infrastructure is made available to the generalpublic or a large industry group and is owned by an organization sellingcloud services.

Hybrid cloud: the cloud infrastructure is a composition of two or moreclouds (private, community, or public) that remain unique entities butare bound together by standardized or proprietary technology thatenables data and application portability (e.g., cloud bursting forload-balancing between clouds).

A cloud computing environment is service oriented with a focus onstatelessness, low coupling, modularity, and semantic interoperability.At the heart of cloud computing is an infrastructure comprising anetwork of interconnected nodes.

Referring now to FIG. 7, illustrative cloud computing environment 1000is depicted. As shown, cloud computing environment 1000 comprises one ormore cloud computing nodes 100 with which local computing devices usedby cloud consumers, such as, for example, personal digital assistant(PDA) or cellular telephone 1000A, desktop computer 1000B, laptopcomputer 1000C, and/or automobile computer system 1000N may communicate.Nodes 100 may communicate with one another. They may be grouped (notshown) physically or virtually, in one or more networks, such asPrivate, Community, Public, or Hybrid clouds as described hereinabove,or a combination thereof. This allows cloud computing environment 1000to offer infrastructure, platforms and/or software as services for whicha cloud consumer does not need to maintain resources on a localcomputing device. It is understood that the types of computing devices1000A-N shown in FIG. 7 are intended to be illustrative only and thatcomputing nodes 100 and cloud computing environment 1000 can communicatewith any type of computerized device over any type of network and/ornetwork addressable connection (e.g., using a web browser).

Referring now to FIG. 8, a set of functional abstraction layers 1100provided by cloud computing environment 1000 (FIG. 7) is shown. Itshould be understood in advance that the components, layers, andfunctions shown in FIG. 8 are intended to be illustrative only andembodiments of the invention are not limited thereto. As depicted, thefollowing layers and corresponding functions are provided:

Hardware and software layer 1102 includes hardware and softwarecomponents. Examples of hardware components include: mainframes; RISC(Reduced Instruction Set Computer) architecture based servers; storagedevices; networks and networking components. In some embodiments,software components include network application server software.

Virtualization layer 1104 provides an abstraction layer from which thefollowing examples of virtual entities may be provided: virtual servers;virtual storage; virtual networks, including virtual private networks;virtual applications and operating systems; and virtual clients.

In one example, management layer 1106 may provide the functionsdescribed below. Resource provisioning provides dynamic procurement ofcomputing resources and other resources that are utilized to performtasks within the cloud computing environment. Metering and Pricingprovide cost tracking as resources are utilized within the cloudcomputing environment, and billing or invoicing for consumption of theseresources. In one example, these resources may comprise applicationsoftware licenses. Security provides identity verification for cloudconsumers and tasks, as well as protection for data and other resources.User portal provides access to the cloud computing environment forconsumers and system administrators. Service level management providescloud computing resource allocation and management such that requiredservice levels are met. Service Level Agreement (SLA) planning andfulfillment provide pre-arrangement for, and procurement of, cloudcomputing resources for which a future requirement is anticipated inaccordance with an SLA. Node ordering provides a way to efficientlyresolve conflicts while ordering nodes within a graph.

Workloads layer 1108 provides examples of functionality for which thecloud computing environment may be utilized. Examples of workloads andfunctions which may be provided from this layer include: mapping andnavigation; software development and lifecycle management; virtualclassroom education delivery; data analytics processing; and transactionprocessing.

The descriptions of the various embodiments of the present inventionhave been presented for purposes of illustration, but are not intendedto be exhaustive or limited to the embodiments disclosed. Manymodifications and variations will be apparent to those of ordinary skillin the art without departing from the scope of the describedembodiments. The terminology used herein was chosen to best explain theprinciples of the embodiments, the practical application or technicalimprovement over technologies found in the marketplace, or to enableothers of ordinary skill in the art to understand the embodimentsdisclosed herein.

What is claimed is:
 1. A method for parallel processing a network ofnodes having at least one ordering constraint and at least one conflictconstraint, the method comprising: breaking a plurality of loops causedby the at least one ordering constraint; determining a node order basedon the at least one ordering constraint; determining a conflict orderbased on the at least one conflict constraint, wherein no new loops arecreated in the network; and performing parallel processing of thenetwork of nodes based on the node order and the conflict order.
 2. Themethod of claim 1, wherein the parallel processing comprises noiseanalysis of an electronic network.
 3. The method of claim 2, wherein theat least one conflict constraint comprises a coupling between a pair ofnets.
 4. The method of claim 1, wherein the conflict order comprisesdetermining an estimated processing cost for an endpoint node associatedwith the at least one conflict constraint.
 5. The method of claim 4,wherein the estimated processing cost comprises an apportionedprocessing cost of a plurality of downstream nodes and wherein theplurality of downstream nodes are downstream of the endpoint node. 6.The method of claim 1, wherein the conflict order comprises determininga criticality value for an endpoint node associated with the at leastone conflict constraint.
 7. The method of claim 1, wherein the nodeorder comprises a partial node order and a strict node order and whereinthe strict node order is based on the partial node order.
 8. A computersystem for parallel processing a network of nodes having at least oneordering constraint and at least one conflict constraint, comprising:one or more processors, one or more computer-readable memories, one ormore computer-readable tangible storage medium, and program instructionsstored on at least one of the one or more tangible storage medium forexecution by at least one of the one or more processors via at least oneof the one or more memories, wherein the computer system is capable ofperforming a method comprising: breaking a plurality of loops caused bythe at least one ordering constraint; determining a node order based onthe at least one ordering constraint; determining a conflict order basedon the at least one conflict constraint, wherein no new loops arecreated in the network; and performing parallel processing of thenetwork of nodes based on the node order and the conflict order.
 9. Thecomputer system of claim 8, wherein the parallel processing comprisesnoise analysis of an electronic network.
 10. The computer system ofclaim 9, wherein the at least one conflict constraint comprises acoupling between a pair of nets.
 11. The computer system of claim 8,wherein the conflict order comprises determining an estimated processingcost for an endpoint node associated with the at least one conflictconstraint.
 12. The computer system of claim 11, wherein the estimatedprocessing cost comprises an apportioned processing cost of a pluralityof downstream nodes and wherein the plurality of downstream nodes aredownstream of the endpoint node.
 13. The computer system of claim 8,wherein the conflict order comprises determining a criticality value foran endpoint node associated with the at least one conflict constraint.14. The computer system of claim 8, wherein the node order comprises apartial node order and a strict node order and wherein the strict nodeorder is based on the partial node order.
 15. A computer program productfor parallel processing a network of nodes having at least one orderingconstraint and at least one conflict constraint, comprising: one or morecomputer-readable storage medium and program instructions stored on atleast one of the one or more tangible storage medium, the programinstructions executable by a processor, the program instructionscomprising: program instructions to break a plurality of loops caused bythe at least one ordering constraint; program instructions to determinea node order based on the at least one ordering constraint; programinstructions to determine a conflict order based on the at least oneconflict constraint, wherein no new loops are created in the network;and program instructions to perform parallel processing of the networkof nodes based on the node order and the conflict order.
 16. Thecomputer program product of claim 15, wherein the parallel processingcomprises noise analysis of an electronic network.
 17. The computerprogram product of claim 16, wherein the at least one conflictconstraint comprises a coupling between a pair of nets.
 18. The computerprogram product of claim 15, wherein the conflict order comprisesdetermining an estimated processing cost for an endpoint node associatedwith the at least one conflict constraint.
 19. The computer programproduct of claim 18, wherein the estimated processing cost comprises anapportioned processing cost of a plurality of downstream nodes andwherein the plurality of downstream nodes are downstream of the endpointnode.
 20. The computer program product of claim 15, wherein the conflictorder comprises determining a criticality value for an endpoint nodeassociated with the at least one conflict constraint.